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This paper proposes a fast and accurate method for sparse regression in the presence of missing data. The underlying statistical model encapsulates the low-dimensional structure of the incomplete data matrix and the sparsity of the…
Least-squares approximation is one of the most important methods for recovering an unknown function from data. While in many applications the data is fixed, in many others there is substantial freedom to choose where to sample. In this…
Small area estimation has received enormous attention in recent years due to its wide range of application, particularly in policy making decisions. The variance based on direct sample size of small area estimator is unduly large and there…
We discuss a class of difference-based estimators for the autocovariance in nonparametric regression when the signal is discontinuous (change-point regression), possibly highly fluctuating, and the errors form a stationary $m$-dependent…
The tuning parameter selection strategy for penalized estimation is crucial to identify a model that is both interpretable and predictive. However, popular strategies (e.g., minimizing average squared prediction error via cross-validation)…
A novel regression method is introduced and studied. The procedure weights squared residuals based on their magnitude. Unlike the classic least squares which treats every squared residual equally important, the new procedure exponentially…
Nonparametric methods are widely applicable to statistical inference problems, since they rely on a few modeling assumptions. In this context, the fresh look advocated here permeates benefits from variable selection and compressive…
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…
Model averaging methods have become an increasingly popular tool for improving predictions and dealing with model uncertainty, especially in Bayesian settings. Recently, frequentist model averaging methods such as information theoretic and…
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…
Consider a regression model with infinitely many parameters and time series errors. We are interested in choosing weights for averaging across generalized least squares (GLS) estimators obtained from a set of approximating models. However,…
We study a linear high-dimensional regression model in a semi-supervised setting, where for many observations only the vector of covariates $X$ is given with no response $Y$. We do not make any sparsity assumptions on the vector of…
Soft-thresholding is a sparse modeling method that is typically applied to wavelet denoising in statistical signal processing and analysis. It has a single parameter that controls a threshold level on wavelet coefficients and,…
It is well known that Monte Carlo integration with variance reduction by means of control variates can be implemented by the ordinary least squares estimator for the intercept in a multiple linear regression model. A central limit theorem…
Many existing covariate shift adaptation methods estimate sample weights given to loss values to mitigate the gap between the source and the target distribution. However, estimating the optimal weights typically involves computationally…
Driven by several successful applications such as in stochastic gradient descent or in Bayesian computation, control variates have become a major tool for Monte Carlo integration. However, standard methods do not allow the distribution of…
In this paper, a statistical model for panel data with unobservable grouped factor structures which are correlated with the regressors and the group membership can be unknown. The factor loadings are assumed to be in different subspaces and…
Least squares linear regression is one of the oldest and widely used data analysis tools. Although the theoretical analysis of the ordinary least squares (OLS) estimator is as old, several fundamental questions are yet to be answered.…
New local linear estimators are proposed for a wide class of nonparametric regression models. The estimators are uniformly consistent regardless of satisfying traditional conditions of depen\-dence of design elements. The estimators are the…
Model averaging has gained significant attention in recent years due to its ability of fusing information from different models. The critical challenge in frequentist model averaging is the choice of weight vector. The bootstrap method,…